Logarithms ( Math) Solve each problems

If you are given the graph of f f​, how do you find the graph of f −1 f−1​? (a) Reflect it over the x-axis. (b) Reflect it over the y-axis. (c) Reflect it over y​=​x y=x​. (d) Reflect it over y​=−​x y=−x​. Find the exact value of each expression. (a) log 2

64 log2⁡64 (b) log 6 1

36 Find the exact value of each expression. (a) log 8

2 log8⁡2 (b) ln(

e 2 √

) Express the given quantity as a single logarithm. ln(1+ x 2

)+ 1 2

ln​x​−lnsin​x How are the graphs of y​= a x y=ax​ and y​= log a

x y=loga⁡x​ related? (a) They are reflections of each other over the x-axis. (b) They are reflections of each other over the y-axis. (c) None of the above. Solve each equation for x x​. (a) e 2​x​+3

=2 e2x+3=2 (b)

ln(5−2​x​)=−7

If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after

t

t hours is

n​=​f​(​t​)=100(

2

t​/3

)

n=f(t)=100(2t/3).

(a) Find the inverse of this function (explain its meaning).

(b) When will the population reach 50,000?

(a)

t​=

t=

(b)

t​=

t= hours (to the nearest tenth)